tailieunhanh - ANALYTIC SOLUTIONS OF ELASTIC TUNNELING PROBLEMS Phần 8

Lực đàn hồi là lực sinh ra khi một vật đàn hồi bị biến dạng. Chẳng hạn, lực gây ra bởi một lò xo khi nó bị nén lại hoặc kéo giãn ra. Lực đàn hồi có xu hướng chống lại nguyên nhân sinh ra nó. | Chapter 8 PREDICTION OF SETTLEMENT TROUGHS Tunneling in urban environments requires the prediction of surface movements in order to asses possible effects on nearby structures. Currently the most commonly used means of making these predictions has been the application of empirical formulas such as the one by Peck 24 . In this chapter Peck s formula will be briefly discussed and compared to the solutions presented in this thesis. It will be shown how the different modes of deformation may be combined and used as a tool for the prediction of settlement troughs. Peck s Surface Settlement Formula Peck s formula for the vertical settlements due to the construction of a tunnel is given by a Gaussian distribution error function curve shown in Figure . The formula for the Gaussian distribution curve as written by Peck is v x - - e x2 2xĩ Xi S 2n where xi is the distance from the center of the symmetrical distribution to the inflection points of the curve shown as points in Figure . The parameter V x h -3-2-10 1 2 3 0 0 . . . . - - - - - - - - - - - v x -1 . . -1 -2 . -2 Figure Peck s formula for xi h 2. 73 74 Prediction of Settlement Troughs Chapter 8 is related to the total area under the curve 7. ỉ v x dx J X. which is equal to the volume of the settlement trough per unit length of the tunnel. The maximum depth of the trough can be determined by setting x 0 in V Vmax v 0 . x z 2n The parameter xi in Peck s formula is determined using empirical design charts see . 24 or formulas see . 2 . A commonly used value is simply xi h 2 as given by Attewell 2 . The volume of the trough V. is usually taken as the estimated ground loss around the tunnel perimeter 24 . It should be emphasized as noted in Chapter 6 that the volume of the settlement trough for the elastic ground loss solution is larger than the amount of ground lost around the tunnel perimeter for values of Poisson s ratio other than . This may .